Archey, Dawn Elizabeth, 1979-
2008-12-20T02:10:58Z
2008-12-20T02:10:58Z
2008-06
http://hdl.handle.net/1794/8155
viii, 107 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *-algebras containing enough projections. The main results of this part of the dissertation are as follows. Let A be a stably finite simple unital C *-algebra and suppose a is an action of a finite group G with the tracial Rokhlin property. Suppose A has real rank zero, stable rank one, and suppose the order on projections over A is determined by traces. Then the crossed product algebra C * ( G, A, Ã Ã Â±) also has these three properties.
In the second portion of the dissertation we introduce an analogue of the tracial Rokhlin property for C *-algebras which may not have any nontrivial projections called the projection free tracial Rokhlin property . Using this we show that under certain conditions if A is an infinite dimensional simple unital C *-algebra with stable rank one and Ã Ã Â± is an action of a finite group G with the projection free tracial Rokhlin property, then C * ( G, A, Ã Ã Â±) also has stable rank one.
Adviser: Phillips, N. Christopher
en_US
University of Oregon
University of Oregon theses, Dept. of Mathematics, Ph.D., 2008;
Mathematics
Cuntz subequivalence
Stable rank one
Tracial Rokhlin property
Finite group actions
Crossed product
C*-algebras
Crossed product C*-algebras by finite group actions with a generalized tracial Rokhlin property
Thesis

Buck, Julian Michael, 1982-
2010-11-30T23:48:55Z
2010-11-30T23:48:55Z
2010-06
http://hdl.handle.net/1794/10849
viii, 113 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
This dissertation consists of four principal parts. In the first, we introduce the tracial quasi-Rokhlin property for an automorphism α of a C *-algebra A (which is not assumed to be simple or to contain any projections). We then prove that under suitable assumptions on the algebra A , the associated crossed product C *-algebra C *([Special characters omitted.] , A , α) is simple, and the restriction map between the tracial states of C *([Special characters omitted.] , A , α) and the α-invariant tracial states on A is bijective. In the second part, we introduce a comparison property for minimal dynamical systems (the dynamic comparison property) and demonstrate sufficient conditions on the dynamical system which ensure that it holds. The third part ties these concepts together by demonstrating that given a minimal dynamical system ( X, h ) and a suitable simple C *-algebra A , a large class of automorphisms β of the algebra C ( X, A ) have the tracial quasi-Rokhlin property, with the dynamic comparison property playing a key role. Finally, we study the structure of the crossed product C *-algebra B = C *([Special characters omitted.] , C ( X , A ), β) by introducing a subalgebra B { y } of B , which is shown to be large in a sense that allows properties B { y } of to pass to B . Several conjectures about the deeper structural properties of B { y } and B are stated and discussed.
Committee in charge: Christopher Phillips, Chairperson, Mathematics;
Daniel Dugger, Member, Mathematics;
Huaxin Lin, Member, Mathematics;
Marcin Bownik, Member, Mathematics;
Van Kolpin, Outside Member, Economics
en_US
University of Oregon
University of Oregon theses, Dept. of Mathematics, Ph. D., 2010;
Dynamical systems
Minimal homeomorphisms
Crossed product algebras
Tracial property
Automorphisms
C*-algebras
Quasi-Rokhlin property
Mathematics
Theoretical mathematics
Crossed product C*-algebras of certain non-simple C*-algebras and the tracial quasi-Rokhlin property
Thesis

Sun, Wei, 1979-
2010-12-22T01:32:21Z
2010-12-22T01:32:21Z
2010-06
http://hdl.handle.net/1794/10912
vii, 124 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
This dissertation is a study of the relationship between minimal dynamical systems on the product of the Cantor set ( X ) and torus ([Special characters omitted]) and their corresponding crossed product C *-algebras.
For the case when the cocyles are rotations, we studied the structure of the crossed product C *-algebra A by looking at a large subalgebra A x . It is proved that, as long as the cocyles are rotations, the tracial rank of the crossed product C *-algebra is always no more than one, which then indicates that it falls into the category of classifiable C *-algebras. In order to determine whether the corresponding crossed product C *-algebras of two such minimal dynamical systems are isomorphic or not, we just need to look at the Elliott invariants of these C *-algebras.
If a certain rigidity condition is satisfied, it is shown that the crossed product C *-algebra has tracial rank zero. Under this assumption, it is proved that for two such dynamical systems, if A and B are the corresponding crossed product C *-algebras, and we have an isomorphism between K i ( A ) and K i ( B ) which maps K i (C(X ×[Special characters omitted])) to K i (C( X ×[Special characters omitted])), then these two dynamical systems are approximately K -conjugate. The proof also indicates that C *-strongly flip conjugacy implies approximate K -conjugacy in this case.
We also studied the case when the cocyles are Furstenberg transformations, and some results on weakly approximate conjugacy and the K -theory of corresponding crossed product C *-algebras are obtained.
Committee in charge: Huaxin Lin, Chairperson, Mathematics
Daniel Dugger, Member, Mathematics;
Christopher Phillips, Member, Mathematics;
Arkady Vaintrob, Member, Mathematics;
Li-Shan Chou, Outside Member, Human Physiology
en_US
University of Oregon
University of Oregon theses, Dept. of Mathematics, Ph. D., 2010;
Tracial rank
Approximate conjugacy
C*-algebras
Minimal dynamical systems
Cantor set
Torus
Mathematics
Theoretical mathematics
Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus
Thesis

Lin, Huaxin
Sun, Michael
2014-09-29T17:46:18Z
2014-09-29T17:46:18Z
2014-09-29
http://hdl.handle.net/1794/18368
In this dissertation we explore the question of existence of a property of group actions on C*-algebras known as the tracial Rokhlin property. We prove existence of the property in a very general setting as well as specialise the question to specific situations of interest.
For every countable discrete elementary amenable group G, we show that there always exists a G-action ω with the tracial Rokhlin property on any unital simple nuclear tracially approximately divisible C*-algebra A. For the ω we construct, we show that if A is unital simple and Z-stable with rational tracial rank at most one and G belongs to the class of countable discrete groups generated by finite and abelian groups under increasing unions and subgroups, then the crossed product A 􏰃ω G is also unital simple and Z-stable with rational tracial rank at most one.
We also specialise the question to UHF algebras. We show that for any countable discrete maximally almost periodic group G and any UHF algebra A, there exists a strongly outer product type action α of G on A. We also show the existence of countable discrete almost abelian group actions with the "pointwise" Rokhlin property on the universal UHF algebra. Consequently we get many examples of unital separable simple nuclear C*-algebras with tracial rank zero and a unique tracial state appearing as crossed products.
en_US
University of Oregon
All Rights Reserved.
C*-algebras
classification
crossed product
existence
group actions
tracial Rokhlin property
The Tracial Rokhlin Property for Countable Discrete Amenable Group Actions on Nuclear Tracially Approximately Divisible C*-Algebras
Electronic Thesis or Dissertation
Ph.D.
doctoral
Department of Mathematics
University of Oregon